The only information about Mirage selection I could find says the it beat the F104. Where the F-5 and F-4 even considered. Either one was in hindsight a better choise. More compatability with closest allies, better weapon upgrades.
The RAAF went through a few phases in its process to select a replacement for the Sabre between 1955-60. The Mirage III was selected in 1960 after a long process with its fair share of significant mistakes by the RAAF and Government.
In 1955 the RAAF assessed aircraft in the US and America and selected the F-104A to replace the Sabre. This went so far as an approved cabinet submission in 1957 for a squadrons worth along with a new medium bomber (Vulcans to replace the Canberra) and the first C-130s. The RAAF only got the C-130 as the Menzies Government was winding down defence at this time (because WWIII with Stalin hadn’t broken out in the mid 50s like they thought it was going to). The RAAF had also turned from the F-104A by this time because of its high sophistication and long takeoff requirement. Cabinet also decided at this time to maintain Australian fighter production (the F-104s were to be imports) and the RAAF got another 30 or so Sabres.
The CAS, Sherger, had wisely established in the late 50s that any new RAAF fighter needed to be able to operate from a runway of less than 3,000 feet (about a km). This was because hundreds of airfields of this length had been built during WWII around SE Asia and longer runways were very rare in our region. The Sabre and F-104 required longer runways. Also a shorter takeoff fighter was likely to have better handling and the RAAF assessed that the Sabre was too demanding for local air forces to operate. The idea of a local production Australian fighter at this time was to not just provide the RAAF with aircraft but in time of general war go into mass production and supply our allies in SEATO.
Anyway by 1959 the Cabinet was willing to order a new fighter and the RAAF went off on another world tour to find one. Before going overseas the RAAF assessed that the three most likely fighters would be the Northrop N156 (later the F-5), the Lockheed F-104G (much improved F-104A) and the Dassault mirage III. Also the English Electric Lightning and Martin F-105 would be looked at but were not considered likely. From this group the selection was narrowed down to the F-10G and the Mirage.
The Mirage was recommended over the F-104G because it could use shorter and softer runways, could fly higher and ferry further and was cheaper. The F-104 was also noted to have pitch up problems, gun gas engine problems, land faster and had a much worse safety record. So the RAAF dodged that bullet and the Mirage was selected.
Another obvious choise is the Hawker Hunter. It was equipped with the RR Avon like both the RAAF's Sabre and Canberra. This commonality was important enough that a trial version of the RAAF's Mirage was fitted with an Avon. It was deemed to expensive although providing superior performance.
The Hunter was from the previous generation and was comparable to the Avon Sabre not the Mirage III. British aviation industry was strongly focused on the high end of combat aircraft for the supersonic generation with the TSR.2, Lightning and Fairey Delta interceptor (cancelled by the Sandays review). They were building the half rocket, half jet Sara SR.177 which would have made an excellent Sabre replacement for the RAAF but it too was cancelled by the Sandays review in 1957.
The Mirage IIIO was first built with the advanced version of the Avon and it was a much better fighter than the Atar 9C powered Mirage III. But Snecma the builders of the Atar underbid their engine to the RAAF and it was selected because it was much cheaper. There is a persistent story supported by other cost records that Snecma made a significant mistake in their cost estimate for the Atar because they did not realise that the Australian Pound had been devalued decades ago in relation to the Pound Sterling. So the RAAF got a cheaper engine and Snecma lost money but since Dassault was thinking that ALL export Mirage IIIs should be built with the Avon maybe Snecma made the ‘mistake’ on purpose.
Did other Mirage operators suffer the same high rate of non combat losses as the RAAF.
Yes. Well those air forces that flew the Mirage as hard as the RAAF did suffered similar peacetime attrition. But the attrition problems with the Mirage were not extreme for the times. The aircraft lost via technical failures were because of engine surging and landing gear failure. Both are the sort of things that could be engineered out so that’s why people are still upset about it. But the F-104G would have been far worse as was seen in its operation with NATO.
Interestingly the Australian built Mirage III was nearly exported twice. To Israel and New Zealand. The Government in 1968 turned down the Israeli request and the Kiwis chose the much cheaper Skyhawk.
As to the hindsight question about the Mirage III it was clearly better for the RAAF than the aircraft it was up against. Weapons compatibility was a non-issue at the time and anyway they used Sidewinders and Mk 80 bombs as their main weapons which were all US standard. However the Mirage III failed to meet Sherger’s runway requirement and was unable to operate from the mass of local airfields. Because they were not used in a general war this wasn’t a major handicap but it would have been if they were really needed.
However there is one plane that was better than the Mirage III and the F-104G and could takeoff and land from short runways. As far as I know it was never assessed by the RAAF. There are 461 pages in the National Archive file on the Sabre Replacement and I haven’t read every one of them yet (you can read them online at their webpage just search for “MP1406/46”). But the Grumman Super Tiger would have been an ideal Sabre replacement for the RAAF. Better at everything than the Mirage III (no engine surge and gear problems) and able to fly from the runways needed. But for some reason, perhaps because it was a Navy plane, it was never looked at. Such is life.